You are conflating two issues, namely symbolic representation vs. continuous recording; and the question of redundancy. Speech output, the stream of speech sounds themselves, is continuous. You can perform various phonetic computations on those waveforms without any segmentation. The claim is, though, that human language handles everything symbolically, so [præŋk] is a discrete symbolic representation that can stand for innumerable instances of the word "prank" in English. I presume that you don't need to be told why this transduction from continuous physical waveforms to discrete symbolic representations is necessary. As a reminder, though, we don't memorize the acoustics of a word when we learn the word, so we don't speak in a high pitched voice if we say a word that we learned from a female. Language (as opposed to speech) presupposes symbolic representations, that is, transcriptions.
As far as the phonemics / phonetic distinction is concerned, you'll need stronger evidence that you've found to show that Roberts has a particular view of the nature of the surface representation. The distinction between a phonemic vs. a phonetic transcription is kind of a red herring in contemporary linguistics. The more important question is, what is the ontology of these objects? Generative grammar (Roberts being an exemplar of the field) holds that a "transcription" is a mental representation, and not a heuristic device. There are competing non-mentalist theories of language where a transcription is simply an operationally defined output. Classically, the taxonomic approach assumes the now fictitious front-end of a perfect transcriber (exemplified by the late Peter Ladefoged and Ian Catford), who could listen to speech and produce a symbolic recording of what appears in that token – they convert actual speech to sequences of phones (sequences of symbols). You can then perform a distributional analysis on those symbols and arrive at a phonemic transcription.
The generative account does not in principle mandate an information-compression step of removing predictable information, though historically we were wedded to the idea of eliminating redundancy. We were definitively not wedded to the spurious phonemic / phonetic distinction of taxonomic theory. But we were certainly wedded to the idea that the output of the syntax can be modified by phonological rules. I presume you don't need to be told why we need phonological rules. In short, your question contains a false presupposition, at least from the generative perspective.